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Questions and Answers
If the hypotenuse of a right triangle is 28 and the length of the side opposite to angle 𝜃 is 17, what is the measure of angle 𝜃?
If the hypotenuse of a right triangle is 28 and the length of the side opposite to angle 𝜃 is 17, what is the measure of angle 𝜃?
- 37.383 (correct)
- 45°
- 30°
- 60°
What is the value of x if the adjacent side is 8 and the angle is 34° in a right triangle?
What is the value of x if the adjacent side is 8 and the angle is 34° in a right triangle?
- 8.52
- 12.63
- 10.94
- 9.18 (correct)
Which expression accurately factors 6𝑥² − 18𝑥 − 24 after factoring out the GCF?
Which expression accurately factors 6𝑥² − 18𝑥 − 24 after factoring out the GCF?
- 6(x + 6)(x - 4)
- 6(x - 4)(x + 1)
- 6(x + 2)(x - 2)
- 6(x - 3)(x + 2) (correct)
If triangle ABC is similar to triangle DEF and AB = 9, DE = 16, and BC = 5, what is the length of EF?
If triangle ABC is similar to triangle DEF and AB = 9, DE = 16, and BC = 5, what is the length of EF?
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In an isosceles triangle with base angles measuring 2𝑥 + 4° and 𝑥 + 36°, what is the value of x?
In an isosceles triangle with base angles measuring 2𝑥 + 4° and 𝑥 + 36°, what is the value of x?
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Study Notes
Right Triangle Calculations
- A right triangle has one 90-degree angle
- To solve for missing variables in right triangles, use trigonometric functions: sine, cosine, and tangent.
- Sine (sin) = Opposite side / Hypotenuse
- Cosine (cos) = Adjacent side / Hypotenuse
- Tangent (tan) = Opposite side / Adjacent side
- Use the inverse trigonometric functions (arcsin, arccos, arctan) to find the angle.
Factoring Algebraic Expressions
- Factoring involves breaking down an expression into the product of its factors.
- Greatest Common Factor (GCF): Find the largest factor common to all terms in the expression and factor it out.
- Factoring Quadratics: For an expression in the form of ax^2 + bx + c, find two numbers whose product is ac and whose sum is b.
- Difference of Squares: A difference of squares is factored as (a + b)(a - b), where a and b are square roots of the squared terms.
Similar Triangles
- Similar triangles have the same shape but different sizes.
- Corresponding angles are equal.
- Corresponding sides are proportional.
- If two triangles are similar, the ratio of corresponding sides is constant.
Probability and Area Model
- Probability is the likelihood of an event occurring.
- Area Model: A visual representation of probabilities using a grid.
- Probability of "And": Multiply the probabilities of the individual events.
- Probability of "Or": Add the probabilities of the individual events, subtracting any overlap.
Isosceles Triangles
- An isosceles triangle has two equal sides and two equal angles.
- The angles opposite the equal sides are also equal.
- The sum of the interior angles of a triangle is 180 degrees.
- Use this information to solve for the missing angles in an isosceles triangle.
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